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We measured the static and dynamic (complex) shear viscosity of a single layer complex plasma by applying, respectively, a stationary and a periodically modulated shear stress induced by the light pressure of manipulating laser beams. Under static conditions the shear viscosity reproduced the numerically predicted shear rate dependence, the so called shear-thinning effect. Under oscillating shear both the magnitude and the ratio of the dissipative and elastic contributions to the complex viscosity show strong frequency dependence. Accompanying molecular dynamics simulations explain and support the experimental observations.

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